In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a prac...In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a practical algorithm for Jordancanonical form J of a quaternion matrix A, but also provide a practical algorithm forcorresponding nonsingular matrix P with P- 1 AP = J.展开更多
矩阵范数是数值计算中误差估计的有力工具,若Q=(qij)为n阶方阵,满足条件: 记所有这样的方阵组成的集合为Q·‖Q‖∞=max sum from j=1 to n|qij|。有人曾经猜想对于任意M>0,存在K（M）>0,使对任意Q∈Q,只要‖e-Q‖∞≤M,就有...矩阵范数是数值计算中误差估计的有力工具,若Q=(qij)为n阶方阵,满足条件: 记所有这样的方阵组成的集合为Q·‖Q‖∞=max sum from j=1 to n|qij|。有人曾经猜想对于任意M>0,存在K（M）>0,使对任意Q∈Q,只要‖e-Q‖∞≤M,就有‖Q‖∞≤K（M）。展开更多
基金Supported by the National Natural Science Foudnation of China and Shanghai Priority Academic Discipline Foundation,Shanghai,China.
文摘In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a practical algorithm for Jordancanonical form J of a quaternion matrix A, but also provide a practical algorithm forcorresponding nonsingular matrix P with P- 1 AP = J.
